Due to the transmission scheduling and packet dropouts, the remote estimator cannot receive all sensor packets at each time.
Let \(\gamma _n(t)=1\)  and 0 denote successful and failed detection of sensor \(n\) 's packet by the remote estimator at time \(t\) .
We also define the age-of-information (AoI) for each sensor,
\(\phi _n(t)\in \mathbb {N}\) , which is the time duration between the previous successful sensor \(n\) 's packet detection and the current time \(t\)  [1]}, i.e.,
\(\phi _n(t) \triangleq \min _{\lbrace t^{\prime }: t^{\prime }<t, \mathbb {1}(\gamma _n(t^{\prime })=1),t^{\prime }\in \mathbb {N}_0\rbrace } t- t^{\prime },\) 
